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IT is an interesting phenomenon that many inventions have 
been made two or more times by different inventors, 
each working without knowledge of the other's research. 
There are a number of cases of such duplicate inventions or 
discoveries that are of common knowledge. It is well known, 
for instance, that both Newton and Leibnitz invented calculus. 
The theory of natural selection was developed practically ident- 
ically by Wallace and by Darwin. It is claimed that both 
Langley and Wright invented the airplane. And we all know 
that the telephone was invented by Gray and by Bell. A good 
many such cases of duplication in discovery are part of the 
stock of knowledge of the general reader. 

There are, however, a large number of very important in- 
stances that are not so well known. For example, the inven- 
tion of decimal fractions is credited to Rudolph, Stevinus and 
Burgi. Oxygen was discovered by Scheele and by Priestley in 
1 774. The molecular theory is due to Avagadro in 1 8 1 1 and 
to Ampere in 1814. Both Cros and du Hauron invented color 
photography in 1869. The trolley car resulted from the work 
of Van Doeple and also Sprague, and the essential elements 
were devised independently by Siemens and Daft. 

We think of Napier and Briggs as the inventors of logarithms, 
but it is not generally known that Burgi also invented them 
three years previously. We associate the origin of photography 
with Daguerre but it was also independently invented by Talbot. 
Boyle's Law is known in French textbooks as Marriotte's Law. 
The existence of Neptune was discovered independently by 
Adams and Leverrier, before the planet was actually observed, 
the work of these two mathematical astronomers leading to its 
observation by others. Gauss is frequently recognized as re- 
sponsible for the principle of least squares. Legendre pub- 
lished his account of the principle three years before Gauss did, 
although Gauss had used the principle still earlier. 



There were four independent discoveries of sunspots, all in 
1611, namely, by Galileo in Italy, Scheiner in Germany, Fabri- 
cius in Holland and Harriott in England. The law of the con- 
servation of energy, so significant in science and philosophy, 
was formulated four times independently in 1847, by Joule, 
Thomson, Colding and Helmholz. They had been anticipated 
by Robert Mayer in 1842. There seem to have been at least 
six different inventors of the thermometer and no less than nine 
claimants of the invention of the telescope. Typewriting 
machines were invented simultaneously in England and in 
America by several individuals in these countries. The steam- 
boat is claimed as the " exclusive " discovery of Fulton, Jouff- 
roy, Rumsey, Stevens and Symmington. 

That so many inventions and discoveries were made by two 
or more persons is not generally known. Researches into the 
histories of science and of inventions reveal a surprisingly large 
number of instances of multiple but independent origins of in- 
ventions. The appendix to this article contains a list of 148 
such cases chosen from the fields of mathematics, astronomy, 
chemistry, physics, medicine, biology, psychology and practical 
mechanics. The list could be extended considerably by further 
research, particularly into the fields of lesser inventions. The 
best source for such data is the history of science within the 
past hundred years. The origin of the vast number of minor 
inventions in the practical arts is not recorded except within 
recent years in the files of the patent offices. 

Knowledge of the origins of inventions in early times is lost. 
Records are largely dependent on writing, and it is only in 
recent years that we have written information about inventors. 
Among the peoples without writing there were probably many 
independent inventions of the same tool. But definite proof is 
difficult to obtain because it is not easy to tell whether the pos- 
session of the same tool by two different primitive groups is 
due to diffusion or to independent origin. In some cases the 
probability of independent origin is very great, as in the case 
of bronze-making in Peru and in the Old World, or the blow- 
gun in America and in Borneo, or the pyramids in Central 
America and in Egypt. A fairly long list of such instances 


might be cited. But a statistical compilation of probable in- 
stances of multiple origins of inventions among primitive peo- 
ples would give little evidence of the relative frequency of in- 
ventions made independently, because of the vast number of 
cases about which we are ignorant. 

But, if we leave these cases out of consideration and confine 
our evidence merely to the historical period, it is surprising 
that we can find SO many cases where two or more inventors 
independently made the same invention, for the development 
of contacts has made the spread of knowledge increasingly 
rapid. For instance, if the knowledge of the invention of wire- 
less telegraphy is spread quickly over all the industrialized 
areas, this fact in itself would cut short the researches of other 
inventors along similar lines. Furthermore, many inventions 
and discoveries are now patented, so that the invention of the 
same object by others either is prevented, or, if not prevented, 
is known. The records of the United States Patent Office 
show that about twice as many patents are applied for as are 
granted. Many of these applications are no doubt denied be- 
cause the invention is already patented. This is further evi- 
dence that many inventions are made independently by more 
than one person. 

For all these reasons a list of recurring independent inven- 
tions assumes a greater importance than would be apparent 
otherwise, and a list of inventions made only once would not 
only be of little significance but would not imply that, without 
the patent laws and rapid dissemination of knowledge, they 
would necessarily have been invented only once. In trying to 
form some estimate, therefore, of the frequency of inventions 
occurring independently more than once, one should remember 
these limitations on the interpretation of the data. 

Bearing in mind all these considerations, the list given in the 
appendix to this article is very impressive. What does it mean? 
Several questions are raised. Are inventions inevitable? If 
the various inventors had died in infancy, would not the inven- 
tions have been made and would not cultural progress have 
gone on without much delay? Are inventions independent of 
mental ability? Is not the determinism in inventions a matter 


of cultural preparation ? Is not social evolution inherent in the 
nature of culture? 

The significance of the phenomenon of parallel occurrences 
of the same inventions has been ably discussed by Dr. A. L. 
Kroeber 1 and the answers to such questions as the foregoing 
have been considered by him. In general, the theory turns on 
two points; that is, there are two factors in the making of in- 
ventions, namely, mental ability and the existing status of 

Mental ability, it is thought, is related to invention in some- 
what the following manner. There is little doubt that inventors 
are men of considerable mental ability, except, perhaps, in 
instances where the accidental element is large. The measure- 
ment of the mental ability of the individuals in any large sample 
of the general population shows a distribution resembling the 
familiar normal probability curve. For any particular mental 
trait there are only a few with large measurements and only a 
few with small measurements and a great many individuals in 
between. The distribution of mental traits is similar, for ex- 
ample, to the distribution of statures, in which there are few 
who are tall and few who are short and many with medium 
stature, the distribution being continuous. Inventors no doubt 
come from the upper portion of such a frequency distribution 
of ability. 

Of course, we do not know just how high up in the scale of 
ability the inventor is found. But in a large sample the normal 
probability curve is such that, in the upper half of the scale of 
ability, will be found half the number of cases. The distribu- 
tion above the upper third of the scale will usually include 
about one-quarter of the cases. That is to say, out of iooo in- 
dividuals about 225 on the average vntt be. found above the 
upper third of the scale; and about 10 will be found above the 
upper tenth of the scale. Thus, even granting that the mental 
ability of the inventor is great, the probabilities are that out of 
a large sample there are many chances of finding more than 

'A. L. Kroeber: "The Superorganic ", American Anthropologist, New Series, 
Vol. 19, No. 2, April-June, 1917, pp. 163-214. 


one person with a high degree of native ability. So that, if an 
inventor had died as an infant, there are chances that there are 
others with just as high native inventive ability. 

But ability may vary over a period of time as well as in a 
cross-section of time. Thus, a random sample of 1000 indi- 
viduals taken 500 years ago may have measured in inherited 
mental traits higher or lower in the scale than 1000 individuals 
chosen today. The average may be greater or less. We are 
here considering native or inherited ability, not the ability that 
results from training. Any high-school boy today knows more 
mathematics than did Aristotle, but his native ability in mathe- 
matics is probably much less. The way this native ability will 
vary over time will be by mutations or by selection. Mutations 
are very infrequent and the process of selection is also slow ; ' 
so that reckoning four generations to the century and consider- 
ing the fact that a biological change or mutation must spread 
to a large number of individuals, there cannot be very much 
variation by groups in inherited mental ability over a few cen- 
turies. Therefore over the few centuries of the historical period, 
or at least over the period for which we can get data on the 
origin of inventions, the variation in native ability according to 
time may in all probability be neglected. There is of course 
— to repeat — variation within a definite sample, but the nature 
of the distribution of native ability is such that there is con- 
siderable probability of finding more than one individual with 
the particular native inventive ability. In fact such native 
ability may be quite plentiful. 

On the other hand, the second factor in invention, the status 
of culture, is obviously highly variable over time, particularly 
in the last few centuries. The material culture three hundred 
years ago was very different from what it is now. It has 
changed rapidly. And the elements of the material culture at 
any one time have a good deal to do with determining the 
nature of the particular inventions that are made. For instance, 

1 This statement is a conclusion based upon a study of the rate of evolution and 
the frequency of mutations. The researches are quite extensive and the limits of 
this paper do not permit a development of the point. 


a few discoveries regarding electricity made possible a great 
many inventions in which these fundamental discoveries were 
used or applied. The many electrical appliances could not 
have been invented in, let us say, the fifteenth century, because 
the fundamental discoveries regarding electricity had not been 
made. A certain cultural preparation was quite necessary for 
the invention of the telegraph. The fact that so many elec- 
trical inventions followed so quickly after certain researches in 
electricity had been made, suggests the inevitability of these 
inventions. And also the fact that most of the major electrical 
inventions were made by two or more inventors leads one to 
think that electrical development was more dependent on cul- 
tural preparation than on genius. Benjamin says in the intro- 
duction to his Age of Electricity: "It is a singular fact that 
probably not an electrical invention of major importance has 
ever been made but that the honor of its origin has been 
claimed by more than one person." I In 1745, Dean von Kleist 
found that by inserting an electrified wire into a phial contain- 
ing spirits of wine, he could store electricity. The same ex- 
periment was made the following year by Cuneus of Leyden, 
and thus we have the fundamental principle of the Leyden jar. 
The French claim that DAlibard was the first to discover the 
identity of lightning and electricity. He performed in May, 
1752, the same experiment that Benjamin Franklin performed 
in June of the same year. The electrical effects of dissimilar 
metals had been noted by Sulzer in 1768 and Cotuguo in 1786, 
but the effective discovery was not made until 1791 when Gal- 
vani independently discovered these same results and evolved 
the principle of the voltaic or galvanic cell, first constructed by 

The successful invention of the telegraph was the culmina- 
tion of many abortive attempts to transmit electricity. The 
first record of any practical form of electric telegraph is de- 
scribed in The Scots Magazine in 1783 in an article supposedly 
written by Charles Marshal. In 1787, Lomond proposed a 
similar but more practical plan. The invention of the galvano- 

1 Park Benjamin : The Age of Electricity, p. iii. 


meter by Ampere and the electro-magnet by Arago then gave 
a tremendous impetus and in 183 1 a young American professor, 
Joseph Henry, constructed the first electro-magnetic telegraph. 
Henry did not patent his idea or make it public, and important 
as the invention was, it remained hidden until Morse performed 
his experiments in 1837 an d finally put his telegraph in opera- 
tion in 1844. It may be questioned whether Morse is entitled 
to the credit for the invention, since he neither first devised the 
mechanism nor originated the alphabet. There were two other 
inventors. Cook and Wheatstone obtained a patent in England 
in 1837, as a result of their joint experiments in constructing a 
telegraph ; and just a month afterward, as a result of independ- 
ent investigations, Steinheil successfully constructed a telegraph 
in Munich. Thus the evolution of electrical science was in the 
direction of the telegraph, and the invention was not dependent 
upon any one inventor. 

Electric motors appeared simultaneously in England, France, 
Germany, Italy and the United States ; and dal Negro, Joseph 
Henry, Bourbonze, McGawley and Davenport all laid claim to 
the invention. Given the railroad and electric motors, is not 
the electric railroad inevitable? At least six different men, 
Davidson, Jacobi, Lilly, Davenport, Page and Hall, claim to 
have made independently the application of electricity to the 
railroad. Similar inquiries show that the development of 
science was leading up to the following inventions, each one of 
which was invented by several different inventors : the induc- 
tion coil, the secondary battery, the electrolysis of water, the 
electro-deposition of metals, the ring armature, the microphone, 
the self-exciting dynamo, the incandescent light and the tele- 
phone. Such a record of electrical inventions, while not nega- 
tiving the factor of mental ability, certainly shows quite impres- 
sively the importance of the cultural factors. 

We realize, of course, that the invention of the steamboat was 
dependent upon the invention of the boat and the invention of 
the steam engine. The dependence of an invention upon its 
constituent elements is a fact. The constituent elements are 
each in turn dependent on their constituent elements, and so on 
back to the ice ages and to resources of nature. But does the 


existence of all the constituent elements of an invention make 
that invention inevitable? Given the boat and the steam en- 
gine, is not the steamboat inevitable ? 

This tendency toward the inevitability of an invention, once 
given the constituent parts, and the dependence of the inven- 
tion on these parts, may be seen in the history of the steam 
engine. 1 One sees in the interesting development of the steam 
engine that this invention was not dependent upon any one man 
and the history indicates that no one man could be expected to 
invent the various constituent parts as preliminary steps to 
making the culminating invention. 

Omitting from consideration the earlier origins of the steam 
engine, we may start with Rivault, who proved in 1605 by ex- 
periment that water confined in a bomb-shell and heated would 
explode the shell. Porta had previously described an appar- 
atus by which the pressure of steam could be made to raise a 
column of water. In 161 5 de Caus constructed a machine 
similar to the one described by Porta. In 1630 Ramseye 
patented a " steam machine." This period was devoted largely 
to speculations as to the possibilities of steam and no further 
practical application was attempted until 1663, when Worcester 
constructed a machine similar to those of Porta and of de Caus, 
and used it to elevate water at Vauxhall. Hautefeuille in 1678 
proposed the use of a piston in the steam engine and Huygens 
first applied this principle. Engines which were a decided im- 
provement on Worcester's were now built. Great interest was 
aroused in their possibilities, and many minds set to work to 
solve the " problem of the steam engine ". An important ad- 
vance was made by Thomas Savery, who in 1698 patented a 
design for the first engine used in pumping water from mines. 
Improvements on Savery's engine were made by Desaguliers in 
1 718, by Blakely and Ridgeley in 1756, and also by Papin 
about this time. Thurston remarks that " at the beginning of 
the eighteenth century, every element of the modern steam en- 
gine had been separately invented and practically applied ".■ 

1 R. H. Thurston: History of the Growth of the Steam Engine. 
» Op. cit., p. 55. 


The nature of the vacuum and the method of obtaining it were 
known. Steam boilers capable of sustaining any desired pres- 
sure had been made. The piston had been utilized and the 
safety valve invented. Thomas Newcomen constructed a new 
type of engine combining these elements instead of attempting 
an improvement on Savery's. His invention was " the engine 
of Huygens with its cylinder and piston as improved by Papin, 
still further improved by Newcomen and Calley by the addi- 
tion of the method of condensation used in the Savery engine ".' 
From Newcomen to Watt there were improvements in propor- 
tions and alterations of details. Watt experimented with the 
Newcomen engine, discovered sources of loss of heat, and set 
about to eliminate this waste. The Watt engine was given its 
distinctive form by 1785, and since that time the growth of the 
steam engine has not been great, the changes being in the 
nature of minor improvements. Contrary to popular impres- 
sion, Watt, great man though he was, does not seem to have 
been indispensable to the perfection of the steam engine. It 
would be an absurdity to conclude that, even if he had died in 
infancy, the Industrial Revolution would not have occurred. 

Our analysis and the list of multiple inventions indicates the 
great importance of the status of culture as a factor in the 
origin of inventions. While it is true that inventions are in 
large part culturally determined, this fact does not mean that 
we can at the present stage of our information predict a partic- 
ular time. In some cases the probability of predicting an in- 
vention is strong as, for instance, in the case of the steamboat, 
which was invented by Fulton eighteen years after the perfec- 
tion of the steam engine in 1 785. But in most cases we do not 
know fully enough the cultural situation determining the inven- 
tion. To say that culture is a determining factor in inventions 
does not tell us what are the particular cultural elements and 
conditions. We do not always know beforehand what the 
necessary constituent cultural elements are that go into the 
making of an invention. 

But even if these elements are in existence and if there is 

1 Op. at., p. 60. 


also the necessary native ability, the mental ability and the con- 
stituent cultural elements must be brought together. Inherent 
ability may exist but it must receive the necessary cultural 
training and it must be applied. The problem has to be seen,. 
its solution socially desired and the ability must be trained and 
stimulated to attack the problem. This is where the idea of 
necessity, so commonly associated with the conception of in- 
ventiveness, comes in. Necessity will not produce an invention 
without the existence of the essential elements. For example, 
there was most urgent necessity among our forefathers not 
many generations ago to cure illness and prevent death. They 
tried magic and the use of herbs ; but the science of medicine 
had not been developed ; the cultural preparation did not exist. 
The need of an invention has a great deal to do with bringing 
ability and the cultural elements together, and is an important 
factor in the process, but there must exist the cultural prepara- 

In conclusion, it is thought that the evidence presented of 
independent duplicate origins of inventions brings out forcibly 
the importance of the cultural factor in the production of in- 
ventions. Such data challenge us to analyze the relation of 
mental ability and cultural preparation as factors in the origin 
of inventions. To say that one of these factors is more import- 
ant than the other is to condense the conclusion to unwarranted 
brevity. It is more satisfactory to summarize briefly the way 
these two factors are related. Mental ability is a factor, since 
no inventions could be made without it. And the mental abil- 
ity of inventors is above the average. But the distribution of 
inherent mental ability at any one time is such that there is 
great probability of considerable frequency of exceptional 
native ability. The manifest ability necessary to produce in- 
ventions may be rare because the native ability has not been 
trained or applied to the problems of inventions. On the other 
hand, a specific invention depends upon a certain cultural pre- 
paration, and could not be made without the existence of the 
constituent cultural elements that make the invention. 

However, if the necessary constituent elements exist, the in- 
vention may occur if there is a cultural need for it, for at any 


one time the distribution of inherent mental ability is such that 
in a large sample there are many cases of exceptional native 
mental ability. Witness the frequency of multiple independent 
inventions. Furthermore, the variation in a result, e. g., in in- 
ventions, depends on the variation of the factors. The factor 
of culture, since the historical period, varies rapidly within very 
short periods of time. The constituent elements of culture at 
any one time are different from what they were a few years 
previously. No such variation is conceivable in inherent mental 
ability over so short a time. In fact, it is exceedingly probable 
that over a few centuries there is no appreciable variation in the 
average or the distribution of inherited mental ability. The 
evidence and analysis show the tremendous importance of the 
cultural factor for inventions. Since the existing status of cul- 
ture is so important a determinant of a succeeding culture, since 
culture is so highly variable, since inherited mental ability is so 
stable, we must conclude that the processes of cultural evolu- 
tion are to be explained in cultural and social terms, that is, in 
terms of sociology and not in terms of biology and psychology. 
William F. Ogburn and Dorothy Thomas. 

Columbia University. 

A List of Some Inventions and Discoveries Made Independently by 
Two or More Persons l 

I. Solution of the problem of three bodies. By Clairaut (1747), Euler (1747) and 
D'Alembert (1747). 

1 The accompanying list of duplicate independent inventions is collected from his- 
tories of astronomy, mathematics, chemistry, physics, electricity, physiology, biology, 
psychology and practical mechanical inventions. The data are thus from the period 
of written records, indeed the last few centuries, and largely from histories of science. 
The various inventions and discoveries vary greatly in their importance. The list 
could be extended by further research. 

There are disputes concerning many of the origins in the instances listed. Disputes 
frequently concern priority, a matter with which the accompanying discussion is not 
concerned. Where a date is doubtful a question-mark has been placed after it. 
Occasionally we have not been able to get the date. The most serious difficulty in 
making the list is the fact that the contribution of one person is in some cases more 
complete than that of another. For instance, Laplace's account of the nebular hypo- 
thesis is in more scientific detail than Kant's. Similarly, Halley's r61e may not have 
been as important as Newton's in formulating the law of inverse squares. It is some- 
times doubtful just where to draw the lines defining a new contribution. Our guides 
hare been the histories of science, and where there are differences in the historical 
accounts we have followed the general practice. The case of the discovery of the 
circulation of the blood we have excluded, as there seems to be a rather wide differ- 


a. Theory of the figure of the earth. By Huygens (1690) and Newton (1680?). 

3. Variability of satellites. By Bradley (1752) and Wargentin (1746). 

4. Motion of light within the earth's orbit. By Delambre (1821?) and Bradley 


5. Theory of planetary perturbations. By Lagrange (1808) and Laplace (1808). 

6. Discovery of the planet Neptune. By Adams (1845) an d Leverrier (1845). 

7. Discovery of sun spots. By Galileo (1611), Fabricius (1611), Scheiner (1611) 

and Harriott (16:1). 

8. Law of inverse squares. By Newton (1666) and Halley (1684). 

9. Nebular hypothesis. By Laplace (1796) and Kant (1755). 

10. Effect of tidal friction on motion of the earth. By Ferrel (1853) and Delaunay 


11. Correlation between variations of sun spots and disturbances on the earth. By 

Sabine (1852), Wolfe (1852) and Gauthier (1852). 

12. Method of getting spectrum at edge of sun's disc. By Jannsen (1868) and 

Lockyer (1868). 

13. Discovery of the inner ring of Saturn. By Bond (1850) and Dawes (1850). 

14. First measurement of the parallax of a star. By Bessell (1838), Struve (1838} 

and Henderson (1838). 

15. The effect of gravitation on movements of the ocean. By Lenz (i845?)'and 

Carpenter (1865). 

16. Certain motions of the moon. By Clairaut (1752), Euler (1752) and D'Alem- 

bert (1752). 


17. Decimal fractions. By Stevinus (1585), Bttrgi (1592), Beyer? (1603) and 

Rttdolff ? (1530). 

18. Introduction of decimal point. By Bttrgi (1592), Pitiscus (1608-12), Kepler 

(1616) and Napier (1616-17). 

19. The equation of the cycloid. By Torricelli (1644) and Roberval (1640). 

20. Logarithms. By Bttrgi (1620) and Napier- Briggs (1614). 

21. The tangent of the cycloid. By Viviani (1660?), Descartes ( 1 660?) and Fermat 


22. Calculus. By Newton (1671) and Leibnitz (1676). 

23. The rectification of the semi-cubical parabola. By Van Heuraet (1659), Neil 

(1657) and Fermat (1657-9). 

ence in the contributions of Cesalpino (1571) and Harvey (1776). Although our rule 
has been to exclude such cases of doubt, in some instances where they have been in- 
cluded we have placed a question mark next to the name. In several cases the in- 
dependence of the research of one claimant has been questioned by another claimant 
or by his followers. In many cases the verdict on the controversy seems to be that 
each of the inventors justly deserves the distinction. Such is the case with the New- 
ton-Leibnitz controversy over calculus, and the Torricelli- Roberval controversy on the 
cycloid. In the case of the microscope, telescope, thermometer, steamboat, electric 
railways and others, claims are still matters of dispute. In a few cases we have in- 
dicated this fact by the words "claimed by" following the subject of the discovery 
or invention. Most of the cases of widely different dates have special explanations 
as in the case of Mendel, and numerous cases where the first inventor does not pub- 
lish his theory until others have come to some conclusions, e. g., there is indisputable 
evidence that Young discovered the principle of interference thirteen years before 
Fresnel, yet neglected to publish it. It has also been difficult to abbreviate the de- 
scription of the discovery into a short title suitable for a list. 


24. Deduction of the theorem on the hexagon. By Pascal (1639), MacLaurin (1719- 

20) and Bessel (1820). 

25. The principle of least squares. By Gauss (1809) and Legendre (1806). 

26. The geometric law of duality. By Foncelet (1838) and Gergone (1838). 

27. The beginnings of synthetic projective geometry. By Chasles (1830) and Steiner 


28. Geometry with an axiom contradictory to Euclid's parallel axiom. By Lobat- 

chevsky (1836-40?), Boylais (1826-33) an d Gauss? (1829). 

29. Lobatchevsky's doctrine of the parallel angle. By Lobatchevsky ( 1840) and 

Saccheri (1733). 

30. Method of algebraic elimination by use of determinants and by dialitic method. 

By Hesse (1842) and Sylvester (1840). 

31. A treatment of vectors without the use of coordinate systems. By Hamilton 

(1843), Grassman (1843) «°d others (1843). 

32. Principle of uniform convergence. By Stokes (1847-8) and Seidel (1847-8). 

33. Logarithmic criteria for convergence of series. By Abel, De Morgan, Bertrand, 

Raabe, Dubamel, Bonnet, Paucker (all between 1832-51). 

34. Radix method of making logarithms. By Briggs (1624), Flower (1771), At- 

wood (1786), Leonelli (1802) and Manning (1806). 

35. Circular slide rule. By Delamain (1630) and Ougbtred (1632). 

36. Method of indivisibles. By Roberval (1640?) and Cavalieri (1635). 

37. Researches on elliptic functions. By Abel (1826-29), Jacob! (1829) and Leg- 

endre (181 1-28). 

38. The double theta functions. By Gopel (1847) and Rosenhain (1847). 

39. The law of quadratic reciprocity. By Gauss (1788-96), Euler (1737) and Leg- 

endre (1830). 

40. The application of the potential function to mathematical theory of electricity 

and magnetism. By Green (1828), Thomson (1846), Chasles, Sturm and 

41. Dirichlet's principle in the theory of potentials. By Dirichlet (1848?) and 

Thomson (1848). 

42. Contraction hypothesis. By H. A. Lorentz (1895) * nd Fitzgerald (1895). 

43. Mathematical calculation of the size of molecules. By Loschmidt and Thompson., 


44. Structure theory. By Butlerow (1888), Kekule ( 1888) and Couper (1888). 

45. Law of gases. By Boyle (1662) and Marriotte (1676). 

46. Discovery of oxygen. By Scheele (1774) and Priestley (1774). 

47. Liquification of oxygen. By Cailletet (1877) and Pictet (1877). 

48. Method of liquefying guies. By Cailletet, Pictet, Wroblowski and Olzewski 

(all between 1877-1884). 

49. Estimation of proportion of oxygen in atmosphere. By Scheele (1778) and 

Cavendish (1781). 

50. Beginnings of modern organic chemistry. By Boerhave (1732) and Hales 


51. Isolation of nitrogen. By Rutherford (1772) and Scheele (1773). 

52. That water is produced by combustion of hydrogen. By Lavoisier-Laplace 

(1783) and Cavendish (1784). 

53. Law of chemical proportions. By Proust (1801-9) and Richter (?). 


54. The periodic law: First arrangement of atoms in ascending series. By De Chan- 

courtois (1864), Newlands (1864) and Lothar Meyer (1864). Law of 
periodicity. By Lothar Meyer (1869) and Mendeleeff (1869). 

55. Hypothesis as to arrangement of atoms in space. By Van 't Hoff (1874) and 

Le Bel (1874). 

56. Molecular theory. By Ampere (1814) and Avagadro (1811). 

57. Hydrogen acid theory. By Davy and Du Long. 

58. Doctrine of chemical equivalents. By Wenzel (1777) and Richter (1792). 

59. Discovery of element of phosphorus. By Brand (1669), Kunckel (1678) and 

Boyle (1680). 

60. Discovery of boron. By Davy (1808-9) a °d Gay-Lussac (1808). 

61. Discovery of ceria. By Hisinger (1803), Berzelius (1803-4) and Klaproth 


62. Process for reduction of aluminum. By Hall (1886), Heroult (1887) and 

Cowles (1885). 

63. Law of mass action of chemical forces. By Jellet (1873), Guldberg-Waage 

(1867), Van't Hoff (1877) and others. 

64. Comparison of refractivity of equimolecular quantities by multiple function. By 

L. V. Lorenz (1880) and H. A. Lorentz (1880). 


65. Resistance of vacuum. By Torricelli-Pascal (1643-6) and von Guericke (1657). 

66. Air gun. By Boyle-Hooke (prior to 1659) and von Guericke ( 1650). 

6j. Telescope. Claimed by Lippershey (1608), Delia Porta (1558), Digges (1571). 

Johannides, Metius (1608), Drebbel, Fontana, Jansen (1608) and Galileo 

458. Microscope. Claimed by Johannides, Drebbel and Galileo (1610?). 

69. Acromatic lens. By Hall (1729) and Dolland (1758). 

70. Principle of interference. By Young (1802) and Fresnel (1815). 

71. Spectrum analysis. By Draper (i860), Angstrom (1854), Kirchoff-Bunsen 

(1859), Miller (1843) and Stokes (1849) 

72. Photography. By Daguerre-Niepe (1839; and Talbot (1839). 

73. Color photography. By Cros (1869) and Du Hauron (1869). 

74. Discovery of overtones in strings. By Nobb-Pigott (1677) and Sauveur 


75. Thermometer. Claimed by Galileo (1592-7?), Drebbel? (1608), Sanctorious 

(1612), Paul(i6i7), Fludd(i6i7), Van Guericke, Porta(i6o6), De Caus 


76. Pendulum clock. Claimed by Bilrgi (1575), Galileo (1582) and Huygens 


77. Discovery of latent heat. By Black (1762), De Luc and Wilke. 

78. Ice calorimeter. By Lavoisier, Laplace (1780) and Black-Wilke. 

79. Law of expansion of gases. By Charles (1783) and Gay-Lussac (1802). 

80. Continuity of gaseous and liquid states of matter. By Ramsay (1880) and Jamin 

■81. Kinetic theory of gases. By Clausius (1850) and Rankine (1850). 
82. Law of conservation of energy By Mayer (1843), Joule (1847), Helmholz 

(1847), Colding (1847) and Thomson (1847). 
83. Mechanical equivalent of heat. By Mayer (1842), Camot (1830), Seguin (1839) 

and Joule (1840). 


84. Principle of dissipation of energy. By Carnot? (1824), Clausius (1850) and 

Thomson (1852). 

85. Law of impact, earlier conclusions. By Galileo (1638) and Marci (1639). 

86. Laws of mutual impact of bodies. ByHuygens (1669), Wallis (1668) and 

Wren (1668). 

87. Apparent concentration of cold by concave mirror. By Porta (1780-91?) and 

Pictet (1780-91?). 

88. Circumstances by which effect of weight is determined. By Leonardo and 


89. Parallelogram of forces. By Newton (1687) and Varignon (1725?). 

90. Principle of hydrostatics. By Archimedes and Stevinus (1608). 

91. Pneumatic lever. By Hamilton (1835) and Barker (1832). 

•92. Osmotic pressure methods. By Van't Hoff (1886) and Guldberg (1870). 

93. Law of inertia. By Galileo, Huygens and Newton (1687). 

94. Machinery for verifying the law of falling bodies. By Laborde, Lippich and 

von Babo. 

95. Center of oscillation. By Bernouilli (1712) and Taylor (1715). 

•96. Leyden jar. By von Kleist (1745) and Cuneus (1746). 

97. Discovery of animal electricity. By Sultzer (1768), Cotuguo (1786) und Gal- 

vani (1791). 

98. Telegraph. By Henry (1831), Morse (1837), Cooke-Wheatstone (1837) and 

Steinheil (1837). 

99. Electric motors. Claimed by Dal Negro (1830), Henry (1831), Bourbonze 

and McGawley (1835). 
*oo. Electric railroad. Claimed by Davidson, Jacobi, Lilly-Colton (1847), Daven- 
port (1835), Page (1850) and Hall (1850-1). 

101. Induction coil. By Page and Ruhmkorff. 

102. Secondary battery. By Ritter and Plante (1859). 

103. Electrolysis of water. By Nicholson -Carlisle (1800) and Ritter. 

104. Method of converting lines engraved on copper into relief. By Jacobi (1839), 

Spencer (1839) and Jordan (1839). 

105. Ring armature. By Pacinotti (1864) and Gramme (i860). 

,106. Microphone. Hughes (1878), Edison (1877-8), Berliner (1877) ">d Blake? 

107. The phonograph. By Edison (1877), Scott? and Cros (1877). 

108. Self-exciting dynamo. Claimed by Hjorth (1866-7), Varley (1866-7), Sie- 

mens (1866-7), Wheatstone (1866-7), Ladd (1866) and Wilde (1863-7). 

109. Incandescent electric light. Claimed by Starr (1846) and Jobard de Clangey 


110. Telephone. By Bell (1876) and Gray (1876). 

111. Arrest of electro-magnetic waves. By Branley (189C-1), Lodge (1893) and 

Hughes (1880). 
•112. Electro-magnetic clocks. By Wheatstone (1845) and Bain (1845). 

113. Printing telegraphs. By Wheatstone (1843) and Bain (1845). 


114. Theory of the infection of micro-organisms. By Fracastoro (1546) and 



115. Discovery of the thoracic duct. By Rudbeck (1651), Jolyff and Bertolinus 


116. That the skull is made of modified vertebrae. By Goethe (1790) and Oken 


117. Nature of the cataract. By Brisseau (1706) and Maitre-Jan (1707). 

118. Operation for cure of aneurisms. By Hunter (1775) and Anil (1772). 

119. Digestion as a chemical rather than a mechanical process. By Spallanzani and 


120. Function of the pancreas. By Purkinje (1836) and Pappenheim (1836). 

121. Solution of the problem of respiration. By Priestley (1777), Scheele (1777), 

Lavoisier (1777), Spallanzani (1777) and Davy (1777). 

122. Form of the liver cells. By Purkinje (1838), Heule (1838) and Dutrochet 


123. Relation of micro-organisms to fermentation and putrefaction. By Latour 

(1837) and Schwann (1837). 

124. Pepsin as the active principle of gastric juice. By Latour (1835) and Schwann 


125. Prevention of putrefaction of wounds by keeping germs from surface of wound. 

By Lister (1867) and Guerin (1871). 

126. Cellular basis of both animal and vegetable tissue. Claimed by Schwann 

(1839), Henle (1839?), Turpin (1839?), Dumortier (1839?), Purkinjfr 
(1839?), Muller (1839?) and Valentin (1839). 

127. Invention of the laryngoscope. By Babington (1829), Liston (1737) and 

Garcia ( 1855). 

128. Sulphuric ether as an anaesthetic By Long (1842), Robinson (1846), Lis- 

ton (1846), Morton (1846) and Jackson (1846). 

129. That all appendages of a plant are modified leaves. By Goethe (1790) and 

Wolfe (1767). 

130. Theory of inheritance of acquired characteristics. By E. Darwin (1794) and 

Lamarck (1801). 

131. Theory of natural selection and variation. By C. Darwin (1858) and Wallace 


132. Laws of heredity. By Mendel (1865), De Vries (1900), Correns (1900) and 

Tscherrnarck (1900). 

133. Theory of mutations. By Korschinsky (1899) and De Vries (1900). 

134. Theory of the emotions. By James (1884) and Lange (1887). 

135. Theory of color. By Young (1801) and Helmholz. 

136. Sewing machine. By Thimmonier (1830), Howe (1846) and Hunt (1840). 

137. Balloon. By Montgolfier (1783), Rittenhouse-Hopkins (1783). 

138. Flying machine. Claimed by Wright (1895-1901), Langley (1893-7) and 


139. Reapers. By Hussey (1833) and McCormick (1834). 

140. Doubly-flanged rail. By Stephens and Vignolet. 

141. Steam boat. Claimed by Fulton (1807), Jouffroy, Rumsey, Stevens and Sym- 

mington (1802). 

142. Printing. By Gutenberg (1443) and Coster (1420-23). 

143. Cylinder printing press. By Koenig-Bensley (1812-13; and Napier (1830). 

144. Typewriter. Claimed by Beach (1847-56), Sholes? (1872) and Wheatstone 


145. Trolley car. By Van Doeple (1884-5), Sprague (1888), Siemens (1881) and 

Daft (1883). 

146. Stereoscope. By Wheatstone (1839) and Elliott (1840J. 

147. Centrifugal pumps. By Appold (1850), Gwynne (1850) and Bessemer (1850). 

148. Use of gasoline engines in automobiles. By Otto (1876), Daimler (1885) and 

Belden (1879?).